Introduction

This is an exercise in response to the ambiguities of articulation
and comprehension of values, whether individually or collectively --
and their strategic implications.

A notable feature is its self-reflexivity -- and consequently its inherent
uncertainty as a necessarily tentative articulation. Partly for that reason,
the arguments are presented in indicative and metaphorical form rather than
being developed "linearly" at any length.

Argument-1

Values: The challenge of values as articulated in value-charged
words is their multiple connotations, whether interpreted in polarized terms
as constructive (positive) values or destructive (negative) values. This challenge
may be addressed by ordering these words in terms of value polarities through
synonyms and antonyms. The value polarities may in turn be clustered as a matrix.
Names (as categories) may be attached to the matrix cells into which
the polarities are clustered.

The problem with this approach to ordering values is related to the increasing
degrees of abstraction -- and consequently to the disassociation and disengagement
with the resulting set. Furthermore, especially when clustered, the value polarities
in any cell tend to imply a more generic form of simple polarity capable of
capturing the implied significance of that cluster as a whole. This then implies
a potentially greater capacity to hold the full relationship between the
polarized extremes than any single term applied in naming the cell cluster.
However, any attempt to apply such a term, or to articulate a more generic
polarization for the cell, immediately falls victim to the challenging ambiguity
of multiple connotations initially addressed.

Hence the merit of an apophatic approach, unsaying or unnaming the cluster.
More generally, hence the merit of the classical Sanskrit adage Neti
Neti (Not this, Not that).

Configuration: A further step towards cognitive engagement
may however be explored by configuring the polarities, rather than holding
them:

in a checklist (whether or not nested)

clustered in cells
in a matrix, for which particular significance is attached to rows and columns

An effort may then be made to transform the matrix to introduce a degree
of curvature indicative of a form of integrative closure. Possibilities include:

a two-dimensional spoked wheel (a symbol favoured by Hinduism and Buddhism)
in which the polarities are assumed to act:

either as spokes

or as elements defining the circumferential rim

a three-dimensional spherically symmetrical polyhedron in which the polarities
are assumed to act

either as edges, as rendered explicit in a tensegrity structure

or as sides ***

dual

Any such configuration raises issues of

the minimum, or optimal, number of elements required to sustain the configuration

the requisite variety of elements, as indicated by their different orientation

the cognitive analogues to the triangulation between elements, interrelating
them -- associated with the transition from linear to curved structures

Paradox and inherent cognitive uncertainty: It is appropriate
to recognize the ambiguity and uncertainty involved in such choices in representational
design. This may relate to the possibility of a form of cognitive uncertainty
principle (Garrison Sposito, Does a generalized Heisenberg Principle
operate in the social sciences? 1969; Gerald Holton,
The Roots of Complementarity, 1970). The
point to be stressed is that there is necessarily also an argument for the
alternative representation appropriately considered to be complementary.

Both paradox and uncertainty have been presented by Kinhide Mushakoji (Global
Issues and Interparadigmatic Dialogue, 1988)
in terms of the logical quadrilemma: A, not-A, A-and-notA, neither-A-nor-notA.

This might be usefully represented in the following pattern of codes.

A

neither-A-
nor-not-A

A-
and-not-A

not-A

The challenge of articulating integrative principles, in contrast with those
based on polarization (or N-fold articulations) has been the subject of a specific
experiment (Distinguishing
Levels of Declarations of Principles, 1980). This highlighted the
manner in which comprehensiveness could best be achieved through the ambiguity
of implicit indication, and that the clarity achieved by explicit articulation
created the challenge of comprehending increasingly larger sets
of more disparate content. This alops makes evident the challenge of satisfactorily
naming such content in that the more definitive the name the less its capacity
to encompass the content.

Another polarity would see the above as the interplay of "fixed" and "mutable".
This might then be understood as a way of articulating the insight of Edward
de Bono (I Am Right, You Are Wrong: New Renaissance: From
Rock Logic to Water Logic. 1990).

the capacity of a 2-dimensional wheel to be partially deformed in contact
with a surface as it rotates, essential to its ability to support a load
through the axle

the dynamics of a spherically symmetrical tensegrity in constant stability-seeking
oscillation around an equilibrium, especially in response to disturbance

the possibility of morphing a symmetrical polyhedron into its dual, in
which nodes become sides and sides are reduced to nodes

Given the importance of alternation in navigating any vehicle (including a
cognitive one) between alternatives, the art is to avoid entrapment by one
or other alternative. This challenge is well represented metaphorically by
the challenge of avoiding plasma quenching in nuclear fusion through its contact
with the sides of the containing vessel. This challenge may be compared with
an analogous one relating to cognitive fusion (Enactivating
a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8),
2006)

Definition and credibility: It follows from the challenge
of uncertainty and necessary alternation that:

closure runs the risk of being premature and therefore a misleading distortion,
whilst necessary in practice and in particular instances:

tentativeness may not be
appropriate when a decision is required, despite the dangers of premature
closure,

This raises the questions of appropriate degrees of:

closure and lightness of touch, perhaps to be understood metaphorically
as the "hardness" or "stickiness" imputed to evidence

Such issues may be expressed in practice, especially within any social group,
in terms of polarities such as:

agreement vs disagreement, namely the degree of elicited agreement, if
any

attachment vs
detachment, namely the degree of attachment to a particular formulation

knowing vs not-knowing, namely the conviction that an insight has been
adequately grasped

Enclosure and emptiness in representation of the whole:
These arguments point to both:

the need for enclosure, as implied by some degree of definition

the role of emptiness, or the undefined, in enabling necessary flexibility
-- and hence the representational value of a wheel or a centro-symmetric polyhedron

The representational process designs and defines a cognitive "space" appropriate
to the uncertainty and underdefinition necessary for cognitive "dancing" to
avoid the sterility of overdefinition and conceptual rigidification. The challenge
of closure has been fruitfully discussed by Hilary Lawson (Closure:
a story of everything, 2001). The need for such a space may be related
metaphorically to the need for shelter from the elements and the efforts to
construct such a protected space.

Indications and coding systems: Whilst the representation
proposed above is essentially geometrical, the corresponding logical challenge
of indication has been extensively explored by George
Spencer-Brown (Laws of Form, 1969/1994). This work
resulted in the development of a calculus of indications (Louis
H. Kauffman,
Virtual
Logic: the calculus of indication, Cybernetics
and Human Knowing: a journal of second order cybernetics and cyber-semiotics, 1998).

In this context it is fruitful to recognize the original value of
"calculus" as a means of handling mathematically the challenge of
relating linear representations as approximations to curves, and its special
significance in "integration" to (*** calculus: indications / circle,
how many pieces for circle integration?)

The concern with logic, and appropriate indication of understanding of
the components of a whole, may be fruitfully explored in terms of the classical
Chinese coding system of 8-trigrams of binary elements configured as a circle
to constitute the BaGua. This might be succinctly described as the minimal
formal codification of differences such as to highlight
degrees of polarization and complementarity -- avoiding problematic use of
words and their confusing connotations (which are separately articulated through
metaphor). As such it constitutes a pattern of associations of requisite systemic
complexity.

Alternative arrangements of trigrams
(BaGua)

Earlier Heaven Arrangement

.

Later Heaven Arrangement

.

William Huff (Homonym, Homonym and Homonym, and Other Word Pairs,
1992) has made creative use of the 8 trigrams to distinguish 8 types of word
pair (such as "peace" and "piece") according to meaning, pronunciation and spelling.
However, his system of associating meaning with the lowest line in the trigram has been reversed
(to the highest), although his coding of same (unbroken line) and different (broken
line) has been retained. He has extended his work to interlingual word pairs.

Categories and cognitive engagement through topoi:
As noted above, value-charged words may be held to carry significance
(peace, love, justice, etc). However, when recognition is accorded to the ambiguity
of their dynamic context through polarization, and such polarities are then
clustered, the degree of abstraction is fundamentally alienating. Cognitive
engagement with such abstractions is highly inhibited.

Centro-symmetrical configuration may elicit a degree of engagement -- as with
the psychoactive function of mandalas. However these typically require enhancement
through emotionally charged symbols -- the topoi of mnemonic techniques.
Use of "topoi", is helpfully contrasted with "topics" as
the essentially neutral derivative through which effort is (vainly) made to
engender the "political will to change". Typically topics, as arrayed for consideration
by a conference for example, are presented as checklists (or in multi-track
tabular programme schedules). As with values treated in this way, they are
indicative of the challenge of cognitive engagement.

This process contrasts with the "scientific" or "logical" approach
to remembering patterned systems of elements -- as perhaps exemplified by the
use of songs
to "re-member" complex metabolic pathways (Harold Baum, Biochemists
Songbook).

It has been argued elsewhere that such mnemonic and aesthetic considerations
have not been applied to arrays of values and strategic initiatives supposedly
fundamental to collective social organization (A
Singable Earth Charter, EU Constitution or Global Ethic? 2006; Structuring
Mnemonic Encoding of Development Plans and Ethical Charters using Musical Leitmotivs,
2001). Put briefly, if people
cannot sing it, how are they to remember it and appreciate its coherence as
a basis for collective action? It is curious that authorities bemoan their
incapacity to enable appropriate change in terms of their inability to engender
the necessary "political will to change" -- whilst simultaneously
extolling the merits of the art and music essential to their cultural identity.

Comprehension and (un)learning: Implicit in this argument
is the role of metaphor in enabling and sustaining comprehension. Hence
the use of the wheel and polyhedral metaphors. Hence the extensive classical
Chinese metaphorical commentary on the trigrams of the BaGua.

The uncertainty as to the appropriate representation, and disagreement regarding
relevant connotations, is indicative of the fundamental challenge of learning
-- of the known in contrast with the (as yet) unknown (or already forgotten).
Ignorance is a necessary reality as is the lack of awareness of that of which
one is ignorant -- and its implications in a global knowledge society subject
to information overload and information underuse. The collective implications
have been explored by John
Ralston Saul (The Unconscious Civilization,
1995).

Self-reflexivity: The more geometrical approach is consistent
with related arguments concerning assumptions made regarding the appropriateness
of the medium on which distinctions are made, as notably developed by the implication
for articulation of more appropriate understanding through "writing" text
on more complex topological surfaces as admirably articulated by Michael Schiltz
(Form
and Medium: a mathematical reconstruction, Image [&] Narrative,
6, 2003) in relation to that calculus of indications. Schiltz notes that form/medium
is "the image for systemic connectivity and concatenation", as described by Humberto
Maturana and Francesco
Varela. Schiltz notes, that the notion of "space" is the key to reflexivity
appropriate to any discussion of form and medium. He draws attention to the additional
value of making such distinctions on a toroidal surface to take into account
issues of self-reflexivity, as discussed elsewhere (Comprehension
of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix
classification onto intertwined tori, 2006).

This presentation might be compared with that of the 4-quadrant AQAL
system of Ken Wilber's
integral movement, except that the emphasis above is on modes or dynamics
of self-reflexive "knowing", whereas the AQAL system is primarily concerned
with statically-defined domains within which knowing takes place.

Argument-2

Cyclic alternation: However the seeming chaotic nature of this alternation
dynamic acquires a degree of coherence when understood as taking place within
a learning cycle of some kind -- perhaps metaphorically to be understood as
a cognitive "dance" of engagement and disengagement with any "other". The BaGua
pattern offers helpful indications regarding the nature of that dance -- the
distinct forms of engagement and disengagement, for example, and their various
degrees of complementarity. It is in this respect that its trigrams might be
understood as specifically indicative as ideograms of certainty and uncertainty,
for example again.

Metaphorically such a cognitive dance is usefully clarified as the various
forms of (dance) step or "gait" that is possible in animal locomotion. Indeed
the movements in the martial art form of BaGua (Baguazhang)
were partially inspired by animal movement. Contrasting movements include:

Analysis of various forms of gait is currently of great interest to the design
of robots and the associated artificial intelligence required for their control
including that of an octapedal spidernauts for
extraterrestrial exploration. An analysis by Oricom Technologies (Analysis
of Multi-Legged Animal + Robot Gaits, 2003) notes, with respect to
of cross-species similarities, that .

species all
across the animal kingdom use legs together in certain combinations that
produce analogous results - namely, "...
1 human leg works like 2 dog legs, 3 cockroach legs and 4 crab legs ...".
In the most basic gait, a human steps from 1 leg to the other, a dog or horse
from 1 diagonal to the other, a roach or beetle from 1 tripod to the other,
and a crab or scorpion from 1 tetrapod to the other. Raibert found a similar
result relating quadruped gaits to a virtual biped gait. Different structures
can work together in functionally-equivalent ways. Although we did not specifically
find it in the literature, it is easy to see how the wave and ripple gaits
of the hexapod shown above can be extended to 8 [or more] legs.

Of related interest are the insights from tensegrity into robot design (John
Rieffel, et. al., Mechanism
as Mind: what tensegrities and caterpillars can teach us about soft robotics, Artificial
Life, 2008). Despite the title of that study, the focus is on robots
with few if any rigid parts, able to substantially deform themselves in order
to flow around, and even through objects. It could however be argued that the
principles being explored might well be applied to the design and operation
of "cognitive vehicles" -- or even "cognitive cyborgs" -- appropriate to the
exploration of the complexities of knowledge space.

But for a biped, for example, the options of each "foot" in octapedal
movement may be engaged in (or disengaged from) as in a dance. Complex dances
may be effectively prefiguring or reinforcing modes of understanding that cannot
otherwise be successfully articulated -- as with the frustration of describing
a spiral staircase without an image. The relationship between human gait and
cognition is currently of interest in medical research (Pamela L. Sheridana,
et. al., The
Role of Higher-Level Cognitive Function in Gait, Dementia
and Geriatric Cognitive Disorders, 2007; Jeffrey M. Hausdorff, Gait
Variability: methods, modeling and meaning, Journal
of NeuroEngineering and Rehabilitation, 2005).

Use of BaGua coding
to indicate 4-fold cognitive modes in relation to 8-fold (tentative)

A

neither-A-
nor-not-A

A-
and-not-A

not-A

A study by B. Svarog (The basic
symmetry of I Ching) is helpful in clarifying the generative operations
of such patterns, notably with the aid of diagrams. With respect to the
suggested cognitive encoding by sonification, through the notes of the
octave corresponding to the trigrams of the BaGua, it is appropriate to
note that from the BaGua were derived the BaYin, the “eight
sounds” -- with which has been associated a Chinese classic Book
of Eight Sounds or Book of Eight Tones (Qī Lín
Bāyīn). These
sounds seem not to have been understood cognitively, although central to
the Chinese cosmology, except perhaps metaphorically as the
eight categories of natural materials out of which musical instruments
were constructed. It was believed that all such categories had to be represented
in ritual music in order to produce music in harmonious accord with nature.
The BaYin system remained the basis for categorizing instruments in China
until the 20th century. Such considerations point to the possibilities
of a form of "cognitive synaesthesia"
(John G. Gammack, Synaesthesia and Knowing, 1999) envisaged by
the composer
Alexander Scriabin as
the next stage of human evolution -- which he sought to enable through
a musical work (Mysterium).

In classical China, a theoretical
system of 12 pitches per octave was generated by Lu-lu pitch pipes
(as from the period of Pythagoras) and considered fundamental to the harmony
of the state. The first frequency of the system was called Huangzhong “Yellow
Bell” which served as the primal generator of the whole series of
twelve. The first of each pair was considered yang or “generating,” the
second as yin or “generated”.

Given the discussion of the metaphorical use of "pillars" as an indication
of values, whether reflected in architecture or not, the musical association
is of interest in that it has been discovered that some pillars in sacred architecture
around the world were specifically "tuned" or placed to enhance (psychoactive)
auditory effects (Ancient
Hindu temples had musical pillars, 2008). Stonehenge has been studied
from that perspective. Arguably designers of modern configurations of pillars
could usefully broaden their perspective.

Curiously however, as illustrated at the time of writing, the conventions
of "political parties" (especially of the greatest democracies) now value highly
the contribution of music and song to the process of giving form to their value-charged
manifestos, eliciting their acceptance and enabling their dissemination. But,
in the process of government itself, such considerations are considered totally
alien -- despite increasing public apathy and antipathy to that process --
especially when there is the expectation that everyone will "sing from the
same hymn sheet". The future may understand matters differently (Aesthetics
of Governance in the Year 2490, 1990; Martin Morris, The
Aesthetics of Democracy: cognitive mapping of mind and culture, 2008).

Knowing about knowing: In the above pattern, the upper
line of the trigram of the BaGua (the outer ring), might be understood to
indicate a condition of either knowing (unbroken line) or not-knowing (broken
line) the inner 4-fold condition from which it was generated. This encodes
an indication of self-reflexivity. In that context "knowing" may also be indicative
of a potentially problematic degree of closure in contrast to a degree of openness
associated with "not-knowing".

Curiously -- especially in relation to current evaluation of what was then
so confidently "known" -- there is an indication of aspects of this understanding
in a poem of US Secretary of Defense, Donald
Rumsfeld (as articulated at a Department
of Defense news briefing, 12 February 2002):

The Unknown
As we know,
There are known knowns.
There are things we know
we know.
We also know
There are known unknowns.
That is to say
We know
there are some things
We do not know.
But there are also unknown unknowns,
The ones we don't know
We don't know.

Of even greater potential interest and immediate significance is the metaphoric
correspondence between the BaGua trigrams and the notes in a musical octave
(as partially explored in the use of music to accompany movement in Baguazhang
and Tai Ch'i). Such a context highlights the manner in which cognitive engagement
with any
"other" takes place through various forms of musical resonance --
whether singly or through combinations that may be harmonious (or dissonant)
in the moment or over a cycle of time.

Environmental engagement: from bullet points to topoi

Values are denatured as "bullet
points" (as in the ubiquitous Power
Point presentation), however much it is assumed by the empowered
that the unconvinced can be profitably and powerfully "targetted" by
such means (Enhancing
Sustainable Development Strategies through Avoidance of Military Metaphors,
1998). In a global knowledge society it is appropriate to suspect that how
we adjust psychologically to apprehension of problems in "reality" --
as an imbalance of values -- may engender biological illness psychosomatically,
especially if that adjustment is unconscious or denied.

Inequality, injustice, impoverishment and life-threatening conditions
of others far away -- even including other species -- may well be engendering
illness in those who believe they are well insulated from their implications.

Rather than "topics", similarly denatured as "bullet points", there is an
unexplored opportunity to engage with the array of topics in the manner originally
implied by the topoi of mnemonic techniques. It is the associated
sense of coherence and psychoactive engagement that will give strategic significance
to the environment -- through its personal meaning rather than through the
abstractions of "climate change", for example (Playfully
Changing the Prevailing Climate of Opinion: climate change as focal metaphor
of effective global governance,
2005). This of course accords with the views long expressed by indigenous peoples
as documented for the United Nations Environment
Programme by Darrell Posey (Cultural and Spiritual
Values of Biodiversity: a complementary contribution to Global Biodiversity
Assessment, Intermediate Technology, 1999).

Conclusion

There is a curious symptomatic confusion between "values" as recognized:

by science in quantitative measurement

by business and economics in terms of imputed financial worth fundamental
to exchange

The argument endeavours to indicate the merit of shifting the approach to
values and ethics from simplistic checklists and "pillars" that are the currently
favoured structural basis for strategic initiatives and governance. In the
quest to contain and embody elusive values, a fruitful shift might explore
a combination of:

transforming "pillars" to "feet", with their implication for coordinated
movement of a coherent "body" (of values)

recognizing that whilst truth is indeed valued, its nature is many-sided,
as is the case with other fundamental values, and therefore indicates the
merit of a polyhedral configuration of values

recognizing the manner in which two-dimensional "pillars" and "poles" call
for a form of enclosure in three dimensions to create a (many-sided, polyhedral)
body enclosing a sheltered, "unoccupied" space

embodying polarization in such a configuration so as to provide a container
for the paradoxical relationship between complementary values in practice

understanding any such body or configuration of values as a form of cognitive
vehicle appropriate to the exploration of knowledge space

recognizing dynamic modes of alternation in the operation of such a body-vehicle
to hold and interrelate incommensurable (value) perspectives and other forms
of disagreement -- as is implied by the ideal of alternation in democratic
governance

using other than vision-based metaphors to sustain the coherence of the
set of contrasting perspectives -- notably metaphors based on music as a
language more widely meaningful across cultures for that purpose

To the extent that values may be understood as of an order of complexity comparable
to the attractors and repulsors of the complexity sciences, this argument suggests
that, as individual topoi with which people are deeply engaged in
some psychoactive manner, the challenge is then how to give significance to
viable, coherent configurations of such attractors -- with which people can
engage as a whole. Hence the focus on the potential of topology -- to be usefully
contrasted with the problematic value "knots" into which society binds itself.
What indeed makes for the coherence of a set of polarized attractors/repulsors?

In an analysis of the articulation of the campaign positions of Barack Obama
and John McCain, George Lakoff (Don't
Think of a Maverick! 2008) offers valuable insights into the disadvantage
in relating to the electorate of focusing on policy "issues" versus that of engendering
"frames". The latter might be fruitfully understood as corresponding to "topoi",
in contrast with "topics", in that topoi have a quality of strange, psychoactive
attractor/repulsors. For policy coherence eliciting engagement and support however,
the challenge is how to configure a set of such of subtle frameworks.

Description of complexity has much higher probability of being meaningfully
understood if it is embodied in dynamics and topology which the brain is better
able to integrate. It is such forms of psychoactive resonance which would appear
to be the key to eliciting "internal" engagement with the challenges
of the
"external" reality. The "pattern
that connects" the disparate challenges
is in all probability a dynamic pattern in which the correspondences bridging
credibly between the disparate domains are more tenuous than convention habitually
requires (Theories
of Correspondences -- and potential equivalences between them in correlative
thinking, 2007).

Given the classical role in China of the Yellow Bell in ensuring the harmony
of the state with the environment, it is ironic how widespread is the current
use of "keynote speakers" to elicit collective harmony amongst topics and perspectives
at any collective gathering. However...

Given the number of keynote speakers on vital strategic issues,
why can we not hear the music they elicit?

References

Edward de Bono. I Am Right,
You Are Wrong: New Renaissance: From Rock Logic to Water Logic. 1990

Antonio de Nicolas. Habits of Mind: an introduction to the philosophy of education.
Lightning Source, 2000 [review]